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There was a mission that required Arthur to help her present gf, but in the second gameplay, I denied supporting her. Nothing much was there in that mission except assisting a family member of gf.

but in the second gameplay, I denied supporting her.

Why is that? What did she do in the first time? Or is it just because nothing much was there?

Arthur has feelings for her but at the same time he also feels that they can't be together as it is hard for Arthur to leave everything and unite with her

I see.

Arthur is a gang-man hence she (gf) distances from him.

She got a hard reason in that case.